Chemical Weathering of Layered Ni-Rich Oxide Electrode Materials: Evidence for Cation Exchange

Pristine samples of NCM523 were used to prepare electrodes (E1 in Table I) containing a coating of 90 wt% oxide (Toda America), 5 wt% Super C45 carbon black (Timcal) and 5 wt% PVdF (polyvinylidene difluoride, Solef 5130, Solvay) on a 20 μm thick aluminum foil.⁵ The electrodes were exposed to moist air (100% humidity) in a sealed container at 30°C, for one and two months (samples E2 and E3, respectively, in Table I). The 100% humidity was achieved by including an open container of water in the sealed chamber; water droplets formed on the electrode samples during the exposure. For comparison, electrodes were also sealed in a container that did not include an open container of water; sample E5 (in Table I) is a representative from this "room air" experiment after two month exposure. After the (moist air or room air) exposure, all samples were dried in a vacuum oven at 120°C for 24 h. Half cells were assembled from these electrodes (1.6 cm² area) using lithium foil as the counter electrode and an electrolyte solution (Gen 2) with 1.2 M lithium hexafluorophosphate (LiPF₆) in a 3:7 w/w liquid mixture of ethylene carbonate (EC) and ethylmethyl carbonate (EMC). All electrochemical measurements were performed using sealed 2032-type stainless steel coin cells, housed in a constant temperature chamber at 30°C and cycled between 3.0 and 4.5 V. Sample E4 is the electrochemically-relithiated electrode E3 after four 3–4.5 V cycles.

The XRD patterns were obtained at ambient temperature using monochromatic synchrotron radiation with an average wavelength of λ = 0.459268 Å at beam line 11-BM of Argonne's Advanced Photon Source. The electrodes were scraped off the current collector and loaded into sealed vials for examination.⁵⁰ Peak positions in the acquired data were analyzed using the CMPR suite by fitting the peaks to prescribed line shapes⁵¹ and the unit cell was indexed using the TREOR program.⁵² The lists of the fitted Bragg peaks and the inferred Miller indexes are given in Tables S1 and S2 of the Supporting Information. The elucidated cell parameters for the bulk material are given in Table II. Powder spectra were calculated from the reported crystallographic data using Mercury (Version 3.6, CCDC) software.

X-ray photoelectron spectroscopy (XPS) data were obtained on electrode samples with a Kratos Axis Ultra X-ray photoelectron spectrometer under ultrahigh vacuum (10⁻⁹ Torr) conditions and with monochromatic Al K_α (1486.6 eV) radiation as the primary excitation source.⁶ Peak fits of all spectra were performed using the Shirley background correction and Gaussian-Lorentzian curve synthesis. The energy scale was adjusted based on the 285.0 eV peak in the C 1s spectra, which arises from the Super C45 carbon black in the oxide electrodes.

All scanning transmission electron microscopy (STEM) images were obtained using a JEOL JEM-ARM200CF microscope operated at 200 kV at the University of Illinois - Chicago.⁵³ STEM images were collected in three modes: low angle annular dark field (LAADF) imaging, high angle annular dark field (HAADF) imaging, and annular bright field (ABF) imaging. The HAADF (Z-contrast imaging) mode provides images of the higher atomic number (Z) transition metal elements, whereas the ABF mode provides images of elements with low Z, including lithium. The LAADF mode excels in imaging columns of atoms with intermediate Z; images obtained in this mode are also more sensitive to strain contrast. In order to minimize artifacts of sample preparation (that can inadvertently induce strain in the material), only minimal preparation was carried out: specifically, the oxide samples were dispersed into either isopropyl alcohol or acetone, then dried before transfer to a holey carbon TEM grid. We were able to acquire high-quality data on the pristine sample E1. The moisture-exposed oxides (E3, for example) were harder to examine because the samples displayed significant sensitivity to the electron beam, which hampered our ability to collect detailed diffraction and spectroscopy data to complement the imaging results.

The PM7 method^54,55 from MOPAC2016 suite^56,57 was used in the semi-empirical calculations on proton exchange in α-LiCoO₂ and (L)BFGS method was used for geometry optimization. PM7 is the latest implementation of the MNDO/NNDO family of semi-empirical methods that are specially designed for solid and crystalline materials and tested extensively on molecular and ionic solids.^54,55 The motivation for using this approximate method was that the standard density functional methods with Hubbard-U correlations (DFT+U)^58,59 were too time consuming for modeling of a dilute solid solutions; there is also great uncertainty as to what extent the "+U" term can mitigate self-interaction errors in such systems.⁶⁰ To estimate the structural changes due to the cation exchange, a 2 × 2 × 2 supercell (Z = 24 molecules) was generated from the known crystal structure and optimized. This supercell contained six layers of four Li⁺ ions. To study H⁺/Li⁺ substitution, only one of the Li⁺ ions in any given layer was replaced with the proton, so that the cell contained N_H = 1-6 protons. The optimized supercells were compared with the pristine supercell to evaluate changes in the lattice parameters.

All potentials described below are given vs Li/Li⁺. In Figure 1 we compare the first cycle capacity-voltage profiles, from half cells assembled using the pristine electrode (E1) and two humid-air exposed electrodes (E2 and E3), obtained with a ∼11 mA/g (∼C/18) current at 30°C. A brief summary of the electrochemistry data is given in Table I; the specific charge and discharge cell capacities are given per weight of the dry oxide material (mAh/g_oxide). The pristine electrode shows the expected cycling behavior. On charge, the cell voltage rises sharply to 3.68 V reflecting the difficulty of extracting the initial Li⁺ ions from the pristine oxide. Cell capacity then increases gradually with voltage, reaching 219 mAh/g_oxide at 4.50 V. On discharge, the cell voltage decreases rapidly from 4.50 V to 4.48 V before decreasing gradually with capacity until the voltage reaches 3.60 V, then decreases sharply delivering 198 mAh/g_oxide at a voltage of 3.0 V. The sharp drop at 3.6 V reflects the difficulty of inserting Li⁺ ions into an "almost full" layered oxide; previous work has shown that the discharge capacity can be increased by using an extremely slow current or by discharging the cell to lower voltages, such as ∼2.0 V.^61,62

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Cells with electrode samples E2 and E3 show behaviors that are distinctly different from that of the pristine electrode cell. For electrode E2 on charge, cell voltage initially increases to 4.12 V before dipping to ∼4.02 V vs Li/Li⁺, then increases again with capacity, delivering 191 mAh/g_oxide at a voltage of 4.5 V vs Li. For electrode E3 on charge, cell voltage rises even higher to 4.26 V before dipping to ∼4.11 V then increases with capacity delivering 179 mAh/g_oxide at a voltage of 4.5 V vs Li. The charge profiles of both E2 and E3 indicate significant changes to the electrodes on exposure to humid air. The increased voltages for initial extraction of Li⁺ ions, 0.44 V for E2 and 0.58 V for E3 relative to that of the pristine electrode, indicate the presence of species at the oxide particle surfaces that impedes the motion of Li⁺ ions: the following drop in voltage suggests the establishment of a Li⁺ ion conduction pathway that reduces impedance at the particle surface. The lower charge capacities, and the uneven rise in voltage on further removal of Li⁺ ions, suggest modifications to the oxide bulk.

On discharge the cell voltage of E2 abruptly decreases from 4.50 V to 4.43 V, whereas that of E3 decreases from 4.50 V to 4.3 V, again indicating oxide impedance. Both E2 and E3 show gradual declines in voltage to 3.0 V vs Li, delivering 166 mAh/g_oxide and 155 mAh/g_oxide respectively, which are ∼84% and ∼78% that of the E1 cell capacity (Table I). Furthermore, neither E2 or E3 profiles show the sharp drop in voltage below 3.6 V seen for E1; the discharge profiles display a gradual curvature with E2 and E3 showing an additional 25 mAh/g_oxide and 58 mAh/g_oxide below 3.6 V, respectively.

Table I also shows data from sample E5, which is the electrode exposed to room air for two months. The first cycle charge and discharge capacities for E5 are 208 mAh/g_oxide and 187 mAh/g_oxide respectively, which are ∼95% and ∼94% that of the E1 cell capacities, and indicates that electrode performance degrades (albeit to a smaller extent) on exposure to room air. The E5 capacity values are, however, significantly higher than those of sample E3 (Table I), indicating that higher-humidity environments have a far greater detrimental effect on electrode performance.

On further cycling, both E2 and E3 show modifications to their voltage profiles, increased charge and discharge capacities, and higher coulombic efficiencies. For E3, on the fourth cycle, the charge capacity, discharge capacity, and Coulombic efficiency are 175 mAh/g_oxide, 173 mAh/g_oxide and 99%, respectively (see inset table in Figure 2); similar values are obtained for cell E2 (see Figure S1 in SI). These data suggest that the moisture-induced capacity loss of the oxide is partially reversible upon relithiation. This electrochemical cycling behavior can be interpreted as possible evidence for the H⁺/Li⁺ cation exchange during weathering of the NCM oxides that is reversed by the electrochemical stripping of protons and reintercalation of the lithium ions.

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XPS is a surface sensitive technique that provides information on the chemical and electronic state of elements contained in a material. The XPS spectra in Figure 3 were obtained by measuring the kinetic energy and number of electrons escaping from the electrode surface (typically < 5 nm) during irradiation of samples with monochromatic Al K_α X-rays. The various spectra discussed below are from electrodes E1 and E2.

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For E1 the C 1s spectrum (Figure 3a) contains contributions mainly from the C45 carbons (285.0 eV) and PVdF [-(CH₂CF₂)_n] binder (286.3 eV, 291.0 eV); weaker intensities, centered near 289.5 eV, result from carbonate impurities on the oxide particles. For E2, the spectral intensities for both C45 carbons and PVdF are lower than those of E1; the PVdF intensity decrease is also observed in the F 1s spectrum (Figure 3b). Additionally in the latter spectrum, a small intensity increase centered at 686.0 eV indicates the presence of lithium fluoride. Alkaline species, produced by the humid-air exposure, could catalyze dehydrofluorination reactions in the PVdF generating HF that would react with the NCM523 (or Li₂CO₃) to form this LiF.⁶

The most significant differences between E1 and E2 are seen in the O 1s spectra (Figure 3c). For E1, the peak centered at 529.8 eV arises from O²⁻ anions in NCM523. Another broad peak centered at 532.3 eV can be assigned to surface impurities, including Li₂CO₃, which is known to form on similar layered oxides.^20,63 For E2, the 529.8 eV is notably absent indicating that the photoelectrons emitted from the oxide are unable to escape the sample because of a surface film that is > 5 nm thick. This surface film, seen as a broad peak centered at 533 eV, likely contains multiple compounds, including the alkaline species mentioned earlier. Changes were also seen in XPS data obtained in the 46–72 eV range, which includes signals from Li 1s, Mn 3p, Ni 3p, and Co 3p (see Figure S2 in SI). Although the signal-to-noise ratio in this binding energy range is generally low, it is apparent that the TM (Mn, Ni, Co) signal intensities are lower for the humid-air exposed sample (E2), indicating coverage of the oxide particles by surface films. In contrast, the Li 1s intensity is slightly greater, and the peak shows a blueshift, indicating lithium presence in the surface films.

The NCM523 oxide has a granular morphology with 6–20 μm size secondary particles consisting of dozens of sintered submicron primary particle crystallites. Even in the pristine oxide, certain Li⁺ ions are replaced by TM ions close to the surface resulting in a modified crystal structure near the edges. In electrochemically cycled samples, this modified surface layer grows inward toward the bulk as the material loses oxygen.^1,7,64

Figures 4 and 5 show images from sample E3 which was exposed to humid air but not cycled. A striking feature in the images is the directionality of chemical damage. To demonstrate this directionality, a primary particle (located on the periphery of a secondary particle) was chosen for examination, and three regions were imaged: the basal plane facets (Figure 4a), the particle bulk (Figure 4b), and the edge facets (Figure 5). As seen in Figure 4a, there is a thin amorphous coating on the surface, which we interpret as the Li₂CO₃ (or LiHCO₃) suggested by the XPS data. The layered structure of the rhombohedral phase is preserved almost all the way to the boundary with this amorphous coating. Additionally, there is significant strain accumulation in a very thin region of the layered structure adjacent to the amorphous coating (bright LAADF contrast and dark ABF contrast in Figures 4a), whereas the bulk is (in comparison) strain-free (Figure 4b). The particle edges (Figure 5) show the most surface reconstruction, which is as expected because Li⁺ ion diffusion is most facile in such regions. The subsurface regions showed the presence of a new phase (Figures 5, panels a-c) that extended 5–20 nm into the bulk. Similar surface reconstructions were also observed in less-ordered crystallites (see Figure S3 in SI). We will continue our examination of these STEM features in the Discussion.

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Diffraction patterns (entire 2θ range) obtained from samples E1, E3, E4 and E5 are provided in Figure S4 in the SI: as noted earlier sample E4 is the electrochemically-relithiated E3 after four 3–4.5 V cycles, and E5 is the two-month room air exposed sample. Detailed views of specific 2θ ranges are contained in Figures 6 through 8. Our XRD findings can be summarized as follows.

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The predominant contribution to the observed pattern originates from the bulk of the crystalline NCM523 oxide. Approximately eighty reflections extending to the Miller index (3,1,16) (see Table S1) can be indexed using a hexagonal lattice (a = b≠c, α = β = 90° and γ = 120°). The elucidated lattice parameters are comparable to reported values for the material. Due to the extended 2θ range (reaching out to 50°), the accuracy in the estimation of the lattice parameters was ca. 5 × 10⁻⁵ Å for a,b and 3.5 × 10⁻⁵ Å for c, respectively (Table II); this accuracy allowed us to quantify very small changes in these lattice parameters. These changes can also be observed directly by comparing positions of selected peaks.

Figure 6 shows close-ups of (0,0,l) reflections (with l = 3, 6, 9, 12), which are sensitive to changes in the spacing between hexagonal basal planes. Figure 7 shows close-ups of the (1,1,0) and (3,0,0) peaks, which are sensitive to changes in the in-plane interatomic spacing of the basal planes. The unit cell for the humid-air exposed sample E3 contracts by 8.0 × 10⁻³ Å (or −0.056%) in the c-axis, which is reflected as a clear shift toward higher 2θ of all E3 reflections shown in Figure 6. Correspondingly, there is a dilation of the basal planes reflected as an expansion of the a lattice parameter (by 0.74 × 10⁻³ Å or +0.026% for E3) and a shift toward lower 2θ of E3 reflections in Figure 7. Similar, albeit smaller, lattice parameter changes are also observed for E5 (Table II): the c-parameter contracts by 1.6 × 10⁻³ Å (or −0.011%) and the a-parameter expands by 0.07 × 10⁻³ Å or +0.002% on two-month exposure to room air. Upon relithiation (sample E4, Table II), there is expansion along the c-axis (by 5.4 × 10⁻³ Å or +0.038%) and contraction in the (a,b) plane resulting in a smaller a lattice parameter (by 0.91 × 10⁻³ Å or −0.032%); these changes are seen as a shift to lower 2θ of all E4 reflections in Figure 6, and as a shift to higher 2θ of all E4 reflections in Figure 7.

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Interestingly, all reflections of sample E3 are noticeably narrower than the corresponding E1 reflections, as seen in Figures 6–8. The changes in peak width indicate that exposure of the sample to humid air results in strain relaxation in the bulk NCM oxide. Relithiation (sample E4) increases peak width but the peaks remain narrower than the corresponding peaks in sample E1, which indicates that the strain in the E4 oxide bulk is lower than that of the E1 oxide bulk.

There is a consensus in the literature that delithiation of the bulk material, whether it is chemical or electrochemical, results in lattice expansion along the c axis.^1,65,66 As Li⁺ ions migrate out, the repulsion between oxygen atoms in the adjacent TM-O layers causes this expansion.^15,23 Contraction of the unit cell is observed when the oxide is delithiated beyond a threshold value.^65–67 This change is usually accompanied by a poorer cyclability and is attributed to irreversibility in the structure transformations. This mechanism is unlikely in our system because it would necessitate a significant removal of Li⁺ ions from the oxide bulk. Furthermore, delithiation would create trends that are opposite to those we observe. In addition, we note that electrochemical relithiation of E3 results in the reversal of this trend.

An alternative explanation for the observed changes can be found in a H⁺/Li⁺ cation exchange process. Specifically, we suggest that protons generated in Reaction 1 exchange with Li⁺ ions at the oxide surface and migrate throughout the crystal, forming a solid solution. As H⁺ has a smaller radius than Li⁺, it interacts with TM-O layers more strongly, which causes contraction of the stack, while the overall crystal structure remains layered (R-3m). Furthermore, the initially greater strain (broader peaks in sample E1) can be ascribed to Li⁺ vacancies in the oxide bulk, resulting from minute deviations from LiMO₂ stoichiometry. As the protons migrate into the crystal bulk and fill these vacancies, the strain is relieved and the Bragg peaks narrow. We will return to this H⁺/Li⁺ exchange hypothesis in the Discussion.

In addition to the aforementioned changes, long term exposure of the oxide to humid air (sample E3) also results in the emergence of a new set of weak reflections that are shown in Figure 8 and highlighted by green vertical lines. Previous researchers (see the Introduction) also observed these additional XRD signals and assigned them to Li₂CO₃ or a tentative cubic phase in the matrix (indexing was difficult due to poor data quality). The former possibility can be excluded in the present case, as none of the weak extra peaks correspond to lithium carbonate. The extra peaks can be indexed to a cubic unit cell with a = 4.04972 ± 0.00024 Å (Table S2 in SI). This value is within 0.29% of a hypothetical cubic lattice (a = 4.06137 ± 0.00002 Å) whose (1,1,1) planes coincide exactly with the basal planes of the bulk rhombohedral phase. This relationship strongly suggests that the additional peaks correspond to an epitaxial phase.

What is this new crystal phase? One possibility is that it corresponds to bunsenite (NiO, space group F m(-3)m).⁶⁸ However, the lattice parameter (a = 4.178 Å) of NiO is significantly larger than our calculated value; the lattice parameter (a = 4.446 Å) for rock salt MnO is even larger.⁶⁸ The lattice parameter decreases when Li₂O dissolves into NiO to form Li_2xNi_1-xO crystal structures (from a≈4.18 Å for NiO to a≈4.12 Å at 20 at% Li);⁶⁹ however, the observed lattice parameter values are still too high.

Another possibility is that the reflections originate from a double cubic unit cell with a≈8.09 Å. Electrochemical delithiation is known to produce highly disordered spinel phases in the NCM oxides.¹ However, doubling the unit cell introduces additional super-reflections that are not observed in our patterns: for example, a spinel (1,1,1) peak next to a rhombohedral (0,0,3) peak. In principle, if the structure disorder (that is, Li⁺/TM ion exchange) in this spinel phase is sufficiently high, it can eliminate these additional reflections. Both Li₂Co₂O₄ spinel with a = 7.994 Å⁷⁰ and LiMn₂O₄ ^{13, 14} have been reported to form with significant disorder in the positions of TM ions. A wide range of lattice parameters a has been reported for LiMn₂O₄ (8.143 Å,⁷¹ 8.161 Å,⁷¹ 8.223 Å,⁷² 8.246 Å,⁷³ and 8.251 Å⁷⁴) with the lower values corresponding to the highest degree of disorder (where Mn³⁺ ions occupy Li⁺ sites).

Neither the M^IIO (rock salt) nor the disordered LiM₂O₄ (spinel) crystal structures (where M stands for TM ions) provide an adequate explanation for the extra peaks observed. Closer inspection of the peaks in the 2θ ranges around 11.2° and 22.4° in Figure 8 reveals that, relative to the rhombohedral reflections, the cubic (1,1,1) reflection is much more intense than the (2,2,2) reflection. Structure factor considerations presented in section S1, Tables S3 to S5, and Figures S5 and S6 in SI indicate that the average number of electrons per cation, in the cation sublattice of the cubic phase, is between 20.3 and 21.8. This estimate is more consistent with the M^IIO oxide (26.0 electrons per Ni^II in NiO; 24.9 electrons per cation in Ni_0.5Co_0.2Mn_0.3) than disordered Li₂M₂O₄ spinel (13.0 electrons per cation for Co^III; 12.8 electrons per cation in Ni_0.5Co_0.2Mn_0.3). These analyses suggest that the cubic phase corresponds to a rock salt structure in which some of the TM ions are substituted by lighter ions and/or TM vacancies, which will both contract the unit cell. Because Li⁺ ion substitution in NiO cannot fully account for the observed lattice parameter,⁶⁹ we again suggest that (the still lighter) protons replace TM ions in this rock salt phase (see below).

As seen from this examination, exposing NCM523 to humid air has significant effects on its structure and electrochemical properties. These effects include (i) capacity decrease and impedance rise, (ii) partial capacity recovery on relithiation, and (iii) a small lattice contraction in the c-axis direction and dilation in the (a,b) plane of the bulk material. In addition to these changes, a disordered cubic phase is observed by STEM in the subsurface regions and corresponding Bragg peaks are observed in the XRD patterns. Unexpectedly, the exposure to humid air relieves strain present in the pristine rhombohedral NCM oxide.

The formation of the cubic phase is the expected outcome of Li⁺ ion loss and the redox reactions postulated by previous researchers. Our study, however, suggests cation exchange as an additional mechanism. The H⁺/Li⁺ exchange is most likely to occur in the edge regions, as Li⁺ ions from the layers migrate outwards and become integrated into the (bi)carbonate or hydroxide, while protons migrate in the opposite direction (Reactions 1 to 3). Eventually a solid solution is formed across the bulk. During electrochemical cycling these intercalant protons can leave the material, and Li⁺ ions can take their place restoring some of the capacity. We also suggest that strain reduction in the oxide bulk, observed on moist air exposure, results from protons filling residual TM ion vacancies in the pristine material.

Moshtev at al.¹² considered γ-NiOOH as a possible model compound for an H⁺/Li⁺ exchanged material. In this compound, the protons are attached to oxygen atoms in the corners of NiO₆ octahedra. In β- and γ-NiOOH the distance between the Ni-O planes is over 4.6 Å, and in Ni(OH)₂•xH₂O it increases to 7.6 Å, as the water molecules enter the spaces between the protonated Ni-O layers.^28,75 These large lattice parameters seemingly argue against such crystal structures as models of the protonated material in our case; however, if only some of the Li⁺ ions are replaced by H⁺ ions, one can expect contraction rather than expansion, since the smaller proton would interact stronger with the oxygens and in this way more efficiently screen the repulsion between them.

To put this consideration on a more quantitative ground, semiempirical calculations were used to estimate lattice parameters (at T = 0 K) for H⁺/Li⁺ substituted α−LiCoO₂ solid solutions (see Figures 9 and 10 and Table S6 in SI). As expected, for the pristine material our calculations favored a hexagonal unit cell with structural parameters similar to those observed experimentally. Following the line of thought given above, dilute H⁺ solutions were examined by imposing periodic boundary conditions for a 2 × 2 × 2 supercell containing 24 lithium ions arranged in six layers. These Li⁺ ions were replaced by one to six protons in such a way that there was only one proton per Li⁺ layer. That leaves multiple ways in which the (several) protons can occupy positions in the layers. The corresponding supercells were geometry optimized, and the lattice parameters, and the standard heats for H⁺/Li⁺ exchange per proton (relative to the pristine material), were estimated.

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Figure 10 and Table S6 in SI summarize computed parameters for the supercells having the lowest electronic energies. It is seen that the c-axis of the supercell systematically contracts as the concentration of protons increases. The standard heat for H⁺/Li⁺ substitution per H⁺ also decreases as the proton concentration increases, which indicates that the occurrence of this cation exchange makes it easier for more protons to enter the lattice. According to these estimates, the observed degree of lattice contraction in sample E3 would correspond to exchanging 5–8 mol% of the Li⁺ ions by protons. Figure 9 shows the (periodic) structure of the supercell containing a single proton in one of the Li⁺ ion layers. The proton is attached to the corner oxygen in one of the CoO₆ octahedra in such a way that the O-H bond makes an acute angle with the plane of the oxygens in the layer. According to the density functional theory models of Kazimirov et al.,⁷⁵ this arrangement is also the way in which O-H bonds are oriented in the monoclinic β-NiOOH (see Figure S7 in SI); in this sense (and this sense only) the latter is a good model for the proton-exchanged α-LiCoO₂.

In this section we argue that the postulated H⁺/Li⁺ exchange not only accounts for the changed properties of the bulk material, but also provides a natural rationale for the observed properties of the cubic phase as observed by STEM and XRD. As the Li⁺ ions migrate to the surface and the protons migrate into the bulk, some of the lattice oxygens in the subsurface regions are tied in the lithium (bi)carbonate formed on the surface. Consequently, a metal-deficient oxide is left behind in the subsurface regions, and the protons can fill these metal-ion vacancies to maintain the overall +2 oxidation state. The result would be a disordered H_2xM_1-xO material_. Structure factor considerations in section S1 in SI suggest that x∼10–20% would provide the best agreement with the experimental results. Both the TM ion vacancies, and H⁺ substitution of the metal ions, reduce the cubic lattice parameter vs. the pristine MO oxide.

In STEM images of the basal planes (Figure 4a) a thin strained region is observed near the particle surfaces. If we assume that this strained region has a cubic character then on moving from the bulk rhombohedral to the cubic phase, the interplanar spacing would change from c_rhom/12 ≈ 1.187 Å to a_cubic/2√3 ≈ 1.169 Å, while the in-plane interatomic distances do not change. This change in spacing is equivalent to a 1.5% compressive strain on the surface region, which would explain the strain contrast in Figure 4a. The epitaxial constraint reduces the formation energy of the TM ion vacancies and H⁺ substitution in the cubic phase.

More interestingly, it appears that exactly the same cubic phase is observed near the basal plane edges (Figure 5, panels a-c). The presence of a thicker reconstructed phase is not surprising by itself since Li⁺ ion diffusion is most facile in these edge regions. However, this cubic phase needs to be the same as the epitaxial phase on the basal planes in Figure 4a, as only one set of cubic XRD reflections is observed in Figure 8. This paradox can be resolved by considering that since (1,1,1) planes of the cubic phase match the basal planes of the rhombohedral phase, any edge facet of the latter would contain an axis belonging to the basal planes. This axis is the zone axis in Figure 5 (that is normal to the printed page); it is shared with the cubic phase and corresponds to the same interatomic spacing. Having only one matched axis allows this cubic phase to grow axiotaxially on the edge facets of the rhombohedral crystals!

We remind the reader that epitaxy occurs when two structures share two linearly independent crystal axes; then both crystal structures can grow on top of each other, with the interfacial plane defined by the two common axes, as is the case for the basal planes in Figure 4a. Axiotaxy⁷⁶ occurs when only one lattice axis is in common. An atomic plane containing the common axis can transition from one structure to the other, rotating around the common axis and forming a kink to accommodate the different interplanar spacing in these two crystal structures. The result is an off-normal fiber texture with a rough interface due to the lack of a common crystallographic interfacial plane. Because axiotaxial growth of the cubic phase is possible on all facets, overlap of several orientations of the cubic lattice is expected. This overlap would naturally account for poor contrast in the edge area relative to the bulk rhombohedral phase. Indeed, close inspection of Figure 5 reveals that the basal planes of the bulk rhombohedral phase tilt by a discrete set of angles in different areas of the edge region, which is in agreement with our axiotaxial hypothesis.

This completes our explanation how a single rock salt phase can account for all of the features observed in STEM and XRD data. As argued above, a rock salt Li_xNi_1-xO structure that is commonly postulated for this cubic phase (see the Introduction) fails to fully explain the observed cubic surface structure. Partial H⁺ substitution in the rock salt structure appears to be the only way to obtain realistic electron densities and lattice parameters in this structure as observed experimentally. The same conclusion was reached for the rhombohedral structure.